[Rasch] comparing paired comparison methods

Donald Bacon dbacon at du.edu
Fri Jan 13 03:22:08 EST 2006

Hi Rasch Experts --

   I'm working with paired comparison data characterized by small samples and a somewhat "naturalistic" design: most respondents compare only a few pairs, and I have no control over which pairs they do choose to compare.  Thus some pairs are never compared while other pairs are compared by 20 or 30 respondents (maybe a bit like sporting contests?).  I know Rasch has been successfully applied to situations like this.  I also thought that Thurstone's method may be appropriate, but I believe this method required equal frequencies of paired comparisons (and of course assumes normality).  The Bradley Terry model appears to work fairly well (Firth's add-on package in R); is this mathematically equivalent to Rasch?  I'm also wondering if a Bayesian model might work even better.  


   Does anyone know a good paper that might compare Rasch, Thurstone, Bradley-Terry, and Bayesian approaches, and offer some kind of decision rule on when to use what?


In advance, thanks for any insights or information you might be able to send along.


Don Bacon

Associate Professor of Marketing

Daniels College of Business

University of Denver

dbacon at du.edu, 303-871-2707


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